Leveraged Returns: Using Borrowed Money

Factoring interest into the equation. What is the expected return to the leveraged position?

Imagine that you have the opportunity to invest in a project that requires an initial investment of $100,000 and has an expected return of 9.5%. You only have $40,000, so you borrow the other $60,000 from your rich uncle (nice to have a rich uncle isn't it?).

Now consider risk. How does risk compare in the leveraged position relative to the unleveraged position?

No, this response is incorrect. You pay interest to your uncle, so it has to be deducted from the expected change in cash flows in the numerator of the expected return.

No, this response is incorrect. The expected return is calculated relative to the capital you contributed, not the total investment.

No, this is response is incorrect. In an efficient market, market investors are rewarded for bearing higher risk with a higher expected return, otherwise there is no incentive to bear higher risk.

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No, this is response is incorrect. In an efficient market, market investors are rewarded for bearing higher risk with a higher expected return, otherwise there is no incentive to bear higher risk.

For the __unleveraged position__, the expected return was 9.5% based on a $100,000 initial investment. This means that the expected cash flow at the end of the invest was $$\displaystyle V_1 = V_0(1+r)=100,000(1.095) = 109,500$$. What other info is needed to calculate the expected return to the leveraged position?

No, not quite. There is an effect on the expected return. Think about the difference in the capital at risk between the two scenarios.

No, this response is incorrect. Consider that expected returns are always calculated relative to capital invested _by the investor_.

Correct! The leveraged return is calculated as $$\displaystyle R_L= \frac{R_P \times (V_E + V_B) - (V_B \times r_D)}{V_E} = \frac{(9.5 \% \times (40,000 + 60,000) - (60,000 \times 4 \%)}{40,000} \approx 18\%$$ where $$R_L$$ is leveraged return, $$R_P$$ is the return on the investment, $$V_E$$ is the value of the equity provided, $$V_B$$ is the amount of the borrowed funds, and $$r_D$$ is the interest rate on the debt.

Correct! Intuitively, if the investment has a higher reward, in an efficient market, the investor must also bear greater risk. In this case, the potential exists to lose more money than initially invested. Consider what would happen if the counterparty in the investment defaulted. You would lose your initial investment of $40,000, and you would still owe your uncle $60,000 plus interest. Also, just as the potential reward is amplified, so are potential losses.

Correct, well done! An investment where you have borrowed a portion of invested funds is referred to as a __leveraged position__. The expected return in a leveraged position is higher than in an __unleveraged position__ as the return is calculated based on the capital you have contributed to the position.

No, you'll need the interest rate.

Right!

Compared to investing $100,000 of your own money, what effect does borrowing money have on the expected return?

You need to factor interest owed to your uncle into the calculation. Assume you have to pay him 4% interest to borrow the $60,000 for the duration of the investment. Your uncle is rich, but he's not giving money away.

18%

24%

12%

Risk is the same

Risk is higher in the leveraged position

Risk is lower in the leveraged position

Return volatility

Interest rate

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No effect

Lower expected return

Higher expected return